Abstract

A real-space method using generating integers is used to classify the possible moiré patterns for two equal hexagonal lattices. The result is that the rotations that take (n, m) to (m, n) with n, m relatively prime form the fundamental moiré transformations, and the number of lattice coincidence areas within each supercell is given by (n −m)2. The scheme may be extended to cases where the lattice constants differ. Additionally, we consider a system with a transition metal between the layers of a twisted bilayer of h-BN. We find that the lowest energy configurations for such an arrangement are those at aligned and anti-aligned sites of the moiré pattern, depending on the transition metal, and the low-symmetry sites possess high magnetization.

Abstract

A real-space method using generating integers is used to classify the possible moiré patterns for two equal hexagonal lattices. The result is that the rotations that take (n, m) to (m, n) with n, m relatively prime form the fundamental moiré transformations, and the number of lattice coincidence areas within each supercell is given by (n −m)2. The scheme may be extended to cases where the lattice constants differ. Additionally, we consider a system with a transition metal between the layers of a twisted bilayer of h-BN. We find that the lowest energy configurations for such an arrangement are those at aligned and anti-aligned sites of the moiré pattern, depending on the transition metal, and the low-symmetry sites possess high magnetization.

Abstract

A real-space method using generating integers is used to classify the possible moiré patterns for two equal hexagonal lattices. The result is that the rotations that take (n, m) to (m, n) with n, m relatively prime form the fundamental moiré transformations, and the number of lattice coincidence areas within each supercell is given by (n −m)2. The scheme may be extended to cases where the lattice constants differ. Additionally, we consider a system with a transition metal between the layers of a twisted bilayer of h-BN. We find that the lowest energy configurations for such an arrangement are those at aligned and anti-aligned sites of the moiré pattern, depending on the transition metal, and the low-symmetry sites possess high magnetization.

Abstract

A real-space method using generating integers is used to classify the possible moiré patterns for two equal hexagonal lattices. The result is that the rotations that take (n, m) to (m, n) with n, m relatively prime form the fundamental moiré transformations, and the number of lattice coincidence areas within each supercell is given by (n −m)2. The scheme may be extended to cases where the lattice constants differ. Additionally, we consider a system with a transition metal between the layers of a twisted bilayer of h-BN. We find that the lowest energy configurations for such an arrangement are those at aligned and anti-aligned sites of the moiré pattern, depending on the transition metal, and the low-symmetry sites possess high magnetization.